Relativity, Cosmology, and Time

Black Hole Information Paradox

Before getting to the essential point of whether black hole destroys information or not, it is necessary to clarify the meaning of information in the debate. According to Leonard Susskind, who played a principle role in the debate, entropy is hidden information. This view considers the basic units (or bits) of information to be the microscopic particles, which can be atoms, elementary particles, or down to the smallest unit the size of Planck length (~ 10-33cm). They are hidden because its existence is not known to us. Once we are aware of its presence (such as an electron in a collision experiment), it becomes information, and generates events that we can keep track of. The information is said to be conserved because we can always recover the original event by time reversal operations (at least in theory, which asserts that the laws of physics are the same in both forward and backward time directions, the "Second Law of Thermodynamics" notwithstanding).

According to general relativity anything that crosses the event horizon of a black hole, is trapped inside forever and lost to the outside world. Any information is lost forever once it crosses the event horizon. Such action violates the law about conservation of information in theory.

In spite of his own discovery of Hawking radiation, which can return matter-energy back to the outside world, Hawking himself insists that information would be destroyed by the black hole since the Hawking radiation does not convey any information about the interior.

Critics argue that according to the rule of conservation of information (which is related to the time reversal symmetry), information cannot be destroyed although it may be scrambled (Figure 09xa). But Hawking was sufficiently confident about his position to place a bet with theoretical physicist John Preskill on the fate of the information.

Since then it has been shown that microscopic quantum ripples at the event horizon can encode information inside the black hole (see "Black Hole Entropy", and "Holographic Space-time" ), so there is no mysterious information loss as the black hole evaporates. In 2004, Hawking called a press conference and announced to the world that he had changed his mind. Black holes did not, after all, irreversibly annihilate information. The bet with Preskill was duly settled in the form, appropriately enough, of an encyclopedia.

Figure 09xa Black Hole Information

In late 2006, 't Hooft and Susskind proposed the "Principle of Black Hole Complementarity" in which both sides are correct. For the

outside observer, matter (the elephant in Figure 09xb) would be gradually reduced to thermal radiation at the event horizon (as it takes an infinite time for the elephant to cross such boundary according to observer A) and returns as scrambled information. While for observer B inside the black hole, the elephant crosses the event horizon

into the black hole, nothing untoward happens until the tidal force takes over ... information is forever lost into the singularity (see "Black Hole Space-time").

Meanwhile, other research in superstring theory finds the black hole to be a "fuzzball" (Figure 09y). The modified black hole does not possess a sharp event horizon; information can be stored in the strings and imprinted on outgoing Hawking radiation. Models of black holes from superstring theory also cast doubt on the idea of the singularity (at the center of the black hole). Yet another scheme suggests that information might leak out by means of quantum teleportation between the entangled pair of virtual particles (one of which has escaped while the other is trapped inside the black hole) and the Hawking radiation. However in the theory of loop quantum gravity, it has been shown that the information trapped in a black hole will be unable to escape via Hawking radiation. But it will survive, eventually rejoining the rest of the universe when the black hole evaporates. So it looks unlikely that Hawking will be able to recover his bet.

It seems that Stephen is a compulsory gambler. Another physicist had made a similar wager with him in 1980 about the fate of information falling into a black hole. Figure 09z1 is a copy of the contract together with the eventual concession by him completed with his signature plus a fingerprint. The document is couched in highly technical terms such as S-matrix and $-matrix. In simple language S-matrix is a mathematical entity that allows a process to run backward, thus would retrieve the original information. The $-matrix ($ denotes "NOT" S) is something invented by Stephen to overturn such rule for the case when the process involves a black hole.

Figure 09z1

The verdict of "information wager" was over turned for re-trial in 2013. On closer examination of the involement of entanglement, it is discovered that the emitting particle is forbidden to entangle with both its former partner inside the black hole and the Hawking radiation

at the same time. The paradox can be resolved by severing the link with the twin (inside the black hole), but it is a violent process. The energy holding up the entanglement would incinerate the event horizon with a wall of fire (Figure 09z2). General relativity maintains that crossing over the event horizon should be uneventful but the firewall erects a signpost in violation of this doctrine. Figure 09z3 illustrates the strange episodes surrounding the paradox.

Figure 09z3 BH Firewall

N.B. If the emitting particle becomes entangled with the environment (the Hawking radiation), then it is not maximally entangled with its former partner any more, and polygamy is permitted (see "monogamy").

Anyway, according to such argument the original information paradox is incarnated as either to abandon general relativity (due to the signpost) or to give up quantum theory (due to the quantum entanglement creating the signpost). For the case of firewall, the observer plunging into the black hole will be incinerated instead of crushed to death by tidal force (see insert in Figure 09z3 and Figure 09d). A meeting was convened at CERN on March 2013 to grapple with the issue, but no resolution is in sight so far.

Then a few months later a new idea claims that entanglement of the photon in the Hawking radiation and its twin in the black hole can be replaced by a wormhole (Figure 09z4). Such connection may not be a problem for quantum monogamy in the way that normal entanglement would cause. The firewall could thus be dispensed with this scheme. Accordingly, there could be wormholes permeating over all the universe; what would happen when they encounter something ? would we be sucked into the black holes ? Or the wormholes exist only in the bulk dimensions, then we have to accept the reality of extra-dimensions. It seems that the scenarios are getting more and more bizarre and very difficult to comprehend.

Hawking posted a paper in arXiv on 22 January 2014 claiming that the firewall violates the CPT invariance of quantum gravity. He suggested that gravitational collapse produces apparent horizon but no event horizon behind which information is lost. This proposal is alleged to be supported by ADS-CFT and is the only resolution of the information paradox compatible with CPT. His verdict now is "no information loss". Like so many instances in this episode, the claims neither provide observational evidence nor theoretical prediction.

Essentially, it suggests that in-falling mass (to the black hole) would leave behind soft graviton (very long wavelength gravitational wave) at the event horizon, while the in-falling electric charge would leave behind soft photon (very long wavelength electromagnetic wave) there. It is not clear if the surface (at the event horizon) would be able to contain an infinite amount of such soft hair, but it is a step forward to pinpoint the substance that preserves all the information falling into the black hole.